Ultra-light micro-lattices and a method for forming the same

ABSTRACT

The present invention relates to a micro-lattice and, more particularly, to an ultra-light micro-lattice and a method for forming the same. The micro-lattice is a cellular material formed of interconnected hollow tubes. The cellular material has a relative density in a range of 0.001% to 0.3%, and a density of 0.9 mg/cc has been demonstrated. The cellular material also has the ability to recover from a deformation exceeding 50% strain.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a Non-Provisional Utility Patent Application of U.S. ProvisionalApplication No. 61/524,714, filed on Aug. 17, 2011, entitled,“Architected Ultra-light Micro-lattices: Redefining the Limits ofLow-Density Materials.”

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under Contract No.W91CRB-10-C-0305 awarded by DARPA. The Government has certain rights inthe invention.

BACKGROUND OF THE INVENTION

(1) Field of Invention

The present invention relates to a cellular material and, moreparticularly, to an ultra-light micro-lattice and a method for formingthe same.

(2) Description of Related Art

Low-density materials are often formed by introducing significantporosity into an architected constituent solid. The effective propertiesof these highly porous materials are defined both by their cellulararchitecture (the spatial configuration of voids and solid) and theproperties of the solid constituent (e.g. stiffness, strength, etc.).Some materials that currently exist in the ultra-light regime below 10mg/cc are traditional foams and aerogels. Previously, silica aero gelheld the record for lowest density material at 1 mg/cc (See the List ofCited Literature References, Literature Reference No. 1). However,recent innovations have led to the development of aerographite, which ison record as the lowest density material at 0.2 mg/cc (See LiteratureReference No. 24). Other ultra-light materials include carbon nanotubeaero gel with a density of 4 mg/cc (See Literature Reference No. 2),metallic foams with densities as low as 10 mg/cc (See LiteratureReference Nos. 3 and 4) and polymer foams reaching 8 mg/cc (SeeLiterature Reference Nos. 5 and 6). Such ultra-light materials arehighly desired for specific strength and stiffness, energy absorption,thermal insulation, damping, acoustic absorption, active cooling andenergy storage, and provide excellent solutions for a variety ofmultifunctional applications (See Literature Reference No. 7). Theexisting ultra-low-density materials mentioned above have randomcellular architectures, with mechanical performance dominated by bendingof internal ligaments, resulting in specific properties far below thoseof the bulk constituent (See Literature Reference No. 7). The onlyexception in the ultra-light regime are honeycomb structures, which havea periodic architecture and excellent mechanical properties, but arehighly anisotropic and reach their fabrication limit at ˜10 mg/cc (SeeLiterature Reference No. 8). To maximize the mechanical properties suchas strength, stiffness, and energy absorption of a cellular material fora given constituent solid, cellular architectures must be formed thatare ordered and mechanically efficient. Deshpande et al. havedemonstrated that ligament bending can be suppressed in suitablydesigned ordered, truss-like cellular architectures, resulting instretching dominated mechanical behavior, with a significant increase ineffective elastic modulus and strength (See Literature Reference No. 9).

However, none of the currently available techniques result in a materialwith ultra-low densities (e.g., less than 0.1% relative density) and alattice cellular architecture that can enable a material with thedesired strength and the ability to achieve recoverable deformation.Thus, a continuing need exists for an ultra-light micro-lattice and amethod for forming such a lattice that possesses an ultra-low relativedensity and also possesses the ability to achieve recoverabledeformation.

SUMMARY OF INVENTION

The present invention relates to a micro-lattice and, more particularly,to an ultra-light micro-lattice and a method for forming the same. Themicro-lattice is a cellular material formed of hollow tubes. Thecellular material has an extremely low relative density, in a range of0.001% to 0.3%. Further, the hollow tubes have a diameter such that thediameter is between 10 and 1000 microns. In another aspect, the hollowtubes are formed by tube walls having a wall thickness between 0.01 and2 microns.

As noted herein, the cellular material is capable of dramaticrecoverable deformations. For example, the cellular material is adaptedto recover from deformations in a range of 2% to 90%.

In another aspect, the hollow tubes are formed of a metallic material orformed of a material selected from a group consisting of nickel, zinc,chrome, tin, copper, gold silver, platinum, rhodium, aluminum, aceramic, including, diamond, diamond like carbon, alumina, zirconia, tinoxide, zinc oxide, silicon oxide, silicon carbide, silicon nitride,titanium nitride, tantalum nitride, tungsten nitride, a polymerincluding Parylene™, or any combination or alloy thereof. The inventionincludes any material that can be readily deposited as a thin film onthe polymer templates using a suitable deposition method, non-limitingexamples of such methods include Atomic Layer deposition, Chemical VaporDeposition, Physical Vapor Deposition, Electroplating, Electrolessplating, Electrophoretic Deposition. Other non-limiting examples ofmaterials include metals such as molybdenum, tantalum, titanium, nickel,and tungsten, or ceramics such as Al2O3, HfO2, La2O3, SiO2, TiO2, WN,ZnO, ZrO2, HfC, LaC, WC, ZrC, TaC, or polymers such as poly(p-xylylenes)and functionalized poly(p-xylylenes), e.g. poly(monochloro-p-xylylene),poly(oxymethylene), poly(3,4-ethylenedioxythiophene), functionalpoly(acrylates) and methacrylates, e.g. poly(pentafluorophenylmethacrylate), poly(pyrrole-co-thiophene-3-acetic acid),poly(p-phenylene terephthalamide).

In yet another aspect, the present invention is directed to a method forforming the micro-lattice. The method includes several acts, such asforming a micro-lattice template; coating the micro-lattice templatewith a film of material; and removing the micro-lattice template toleave a cellular material formed of hollow tubes, the cellular materialhaving a relative density in a range of 0.001% to 0.3%.

The micro-lattice template is formed by exposing a photomonomer to acollimated UV light through a patterned mask. The micro-lattice templateis an interconnected three-dimensional open cellular photopolymerlattice.

In another aspect, in coating the micro-lattice template with a film ofmaterial, the film of material is a metal, ceramic, or polymer.Additionally, the micro-lattice template is coated using a techniqueselected from a group consisting of electro-plating, electrophoreticdeposition, chemical vapor deposition, physical vapor deposition, atomiclayer deposition, solution deposition or sol-gel deposition.

Finally and without implying a limitation, in removing the micro-latticetemplate, the micro-lattice template is removed via chemical etching,thereby leaving the cellular material formed of hollow tubes.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects, features and advantages of the present invention will beapparent from the following detailed descriptions of the various aspectsof the invention in conjunction with reference to the followingdrawings, where:

FIG. 1 is an illustration of an ultra-light micro-lattice according tothe present invention;

FIG. 2 is an illustration depicting the size scale and controllablearchitectural features of a micro-lattice according to the presentinvention;

FIG. 3 is an illustration depicting a method for forming an ultra-lightmicro-lattice according to the present invention;

FIG. 4A is an illustration of a micro-lattice sample prior tocompression;

FIG. 4B is an illustration of the micro-lattice sample after a firstcompression;

FIG. 4C is an illustration of the micro-lattice sample, depicting thesample at 50% compression;

FIG. 4D is an illustration depicting the micro-lattice sample after thecompression load is removed, illustrating that the ultra-lightmicro-lattice recovers approximately 98.6% of its original height andresumes its original shape;

FIG. 4E is an optical image of a unit cell of the micro-lattice, in anunloaded or uncompressed condition;

FIG. 4F is an optical image of the unit cell, depicting the unit cell asaccommodating compressive strain by buckling at its nodes;

FIG. 4G is a scanning electron microscopy (SEM) image of a node beforetesting;

FIG. 4H is an SEM image of the node after six compression cycles at 50%strain;

FIG. 5A is a graph illustrating a stress-strain curve measured at aprescribed displacement rate of 10 μm/sec;

FIG. 5B is a graph of illustrating how stiffness and strength diminishwith cycle number;

FIG. 5C is a graph illustrating stress-strain curves of the first twocompression cycles of a sample with a density of 1 mg/cc and larger unitcells (L: 4 mm, D: 500 μm, t: 120 nm);

FIG. 5D is a graph illustrating stress-strain curves of the compressionof a sample with 43 mg/cc (L: 1050 μm, D: 150 μm, t: 1400 nm);

FIG. 5E is an SEM micrograph of post-nanoindentation mark in a 500nm-thick electroless nickel film, demonstrating brittle behavior; and

FIG. 6 is a table including a summary of architecture and properties ofmicro-lattices according to the present invention.

DETAILED DESCRIPTION

The present invention relates to a micro-lattice and, more particularly,to an ultra-light micro-lattice and a method for forming the same. Thefollowing description is presented to enable one of ordinary skill inthe art to make and use the invention and to incorporate it in thecontext of particular applications. Various modifications, as well as avariety of uses in different applications will readily apparent to thoseskilled in the art, and the general principles defined herein may beapplied to a wide range of embodiments. Thus, the present invention isnot intended to be limited to the embodiments presented, but is to beaccorded the widest scope consistent with the principles and novelfeatures disclosed herein.

In the following detailed description, numerous specific details are setforth in order to provide a more thorough understanding of the presentinvention. However, it will be apparent to one skilled in the art thatthe present invention may be practiced without necessarily being limitedto these specific details. In other instances, well-known structures anddevices are shown in block diagram form, rather than in detail, in orderto avoid obscuring the present invention.

The reader's attention is directed to all papers and documents which arefiled concurrently with this specification and which are open to publicinspection with this specification, and the contents of all such papersand documents are incorporated herein by reference. All the featuresdisclosed in this specification, (including any accompanying claims,abstract, and drawings) may be replaced by alternative features servingthe same, equivalent or similar purpose, unless expressly statedotherwise. Thus, unless expressly stated otherwise, each featuredisclosed is only one example of a generic series of equivalent orsimilar features.

Furthermore, any element in a claim that does not explicitly state“means for” performing a specified function, or “step for” performing aspecific function, is not to be interpreted as a “means” or “step”clause as specified in 35 U.S.C. Section 112, Paragraph 6. Inparticular, the use of “step of” or “act of” in the claims herein is notintended to invoke the provisions of 35 U.S.C. 112, Paragraph 6.

Please note, if used, the labels left, right, front, back, top, bottom,forward, reverse, clockwise and counter clockwise have been used forconvenience purposes only and are not intended to imply any particularfixed direction. Instead, they are used to reflect relative locationsand/or directions between various portions of an object.

Before describing the invention in detail, first a list of citedreferences is provided. Subsequently, an introduction provides thereader with a general understanding of the present invention. Next,specific details of the present invention are provided to give anunderstanding of the specific aspects. Finally, the specific details ofa fabrication example are provided to illustrate the generation of anultra-light micro-lattice according to the present invention.

(1) List of Cited Literature References

The following references are cited throughout this application. Forclarity and convenience, the references are listed herein as a centralresource for the reader. The following references are herebyincorporated by reference as though fully set forth herein. Thereferences are cited in the application by referring to thecorresponding literature reference number.

-   1. Guinness Book of World Records, Least Dense Solid, 2003.-   2. J. Zou, J. Liu, A. S. Karakoti, A. Kumar, D. Joung, Q. Li, S. I.    Khondaker, S. Seal, L. Zhai, Ultralight Multiwalled Carbon Nanotuhe    Aerogel, ACS Nano 4 7293-7302 (2010).-   3. A. Verdooren, H. M. Chan,w J. L. Grenestedt, M. P. Harmer,    and H. S. Caram, Fabrication of Low-Density Ferrous Metallic Foams    by Reduction of Chemically Bonded Ceramic Foams, J. Am. Ceram. Soc.    89 3101-3106 (2006).-   4. B. C. Tappan, M. H. Huynh, M. A. Hiskey, D. E. Chavez, E. P.    Luther, J. T. Mang, S. F. Son, Ultralow-Density Nanostructured Metal    Foams: Combustion Synthesis, Morphology, and Composition, J. Am.    Chem. Soc. 128 6589-6594 (2006).-   5. M. Chanda, S. K. Roy, Plastics Technology Handbook (CRC Press,    Boca Raton, Fla., 2007).-   6. BASF Corp., Materials Safety Data Sheet for Basotect V3012 (2007)-   7. L. J. Gibson, M. F. Ashby, Cellular Solids: Structure and    Properties (Cambridge Univ. Press, Cambridge, UK, 1997).-   8. Hexcel Corp., HexWeb™ Honeycomb Attributes and Properties,    (Datasheet, 1999).-   9. V. S. Deshpande, M. F. Ashby, N. A. Fleck, Foam topology bending    versus stretching dominated architectures, Acta Materialia. 49    1035-1040 (2001).-   10. R. S. Lakes, Materials with structural hierarchy. Nature 361    511-515 (1993).-   11. A. J. Jacobsen, W. B. Carter, S. Nutt, Compression behavior of    micro-scale truss structures formed from self-propagating polymer    waveguides. Acta Materialia 55 6724-6733 (2007).-   12. A. J. Jacobsen, W. B. Carter, S. Nutt, Micro-scale Truss    Structures formed from Self-Propagating Photopolymer Waveguides.    Advanced Materials 19 3892-3896 (2007).-   13. A. J. Jacobsen, W. B. Carter, S. Nutt, Shear behavior of polymer    micro-scale truss structures formed from self-propagating polymer    waveguides. Acta Materialia 56 2540-2548 (2008).-   14. S. H. Park, D. N. Lee, A study on the microstructure and phase    transformation of electroless nickel deposits. Journal of Materials    Science 23 1643-1654 (1988).-   15. J. Lian, L. Valdevit, T. A. Schaedler, A. J. Jacobsen, W.    Barvosa-Carter, J. R. Greer, Catastrophic vs. gradual collapse of    thin-walled nanocrystalline Ni cylinders as building blocks of    micro-lattice structures, Nano Letters 11 p.4118 (2011).-   16. S. Y. Chang, Y. S. Lee, H. L. Hsiao, T. K. Chang, Mechanical    properties and deformation behavior of amorphous nickel-phosphorous    films measured by nanoindentation test. Metall Mater Trans A 37A    2939-2945 (2006).-   17. L. G. Brazier, On the Flexure of Thin Cylindrical Shells and    Other “Thin” Sections, Proceedings of the Royal Society of London.    Series A, 116, No. 773 (1927), pp. 104-114.-   18. N. J. Mills, Finite Element Models for the viscoelasticity of    open-cell polyurethane foam, Cellular Polymers 5 293-316 (2006).-   19. A. Cao, P. L, Dickrell, W. G. Sawyer, M. N.    Ghasemi-Nejhad, P. M. Ajayan, Super-Compressible Foamlike Carbon    Nanotube Films. Science 310 1307-1310 (2005).-   20. J. R. Trelewicz, C. A. Schuh, The Hall-Petch breakdown in    nanocrystalline metals: A crossover to glass-like deformation. Acta    Materialia 55 5948-5958 (2007).-   21. W. C. Young, R. G. Budynas, Roark's Formulas for Stress and    Strain (McGraw-Hill, New York ed. 7 2002) p. 735.-   22. J. E. Butler, A. V. Sumant, The CVD of Nanodiamond Materials.    Chem. Vap Deposition 14 145-160 (2008).-   23. G. F. Smits, Effect of Cellsize Reduction on Polyurethane Foam    Physical Properties Reduction. Journal of Building Physics 17    309-329 (1994).-   24. Mecklenburg et al., Aerographite: Ultra Lightweight, Flexible    Nanowall, Carbon Microtube Material with Outstanding Mechanical    Performance, Advanced Materials (2012).-   25. Schaedler, T. A., Jacobsen, A. J., Torrents, A., Sorensen, A.    E., Lian, J., Greer, J. R., Valdevit, L., Carter, W. B., (November,    2011), Ultralight Metallic Microlattices. Science 334, 962-965.

(2) Introduction

The present invention is directed to an ultra-light metallic cellularmaterial that can recover from large deformation. The material is formedof a micro-lattice of hollow tubes with ultra-thin walls (0.1-1 micron).This structure allows for relative densities of 0.01%-0.1% correspondingto 0.9-9 mg/cc for nickel, with a recoverable deformation exceeding 50%,both of which are novel and have not been achieved heretofore.

This invention enables metallic materials that are lighter than anyother previously known material. Aerographite currently holds the recordfor lowest density material at 0.2 mg/cc and metallic foams have heldthe record for lowest density metallic material at 10 mg/cc. With thisinvention, nickel cellular materials have been achieved with a densityof 0.9 mg/cc. It should be noted that the approach of the presentinvention can be used to generate materials with even lower densities,as described below.

Additionally, the present invention allows for the generation ofmetallic materials that can withstand and recover from deformations upto and exceeding 50%. This is an improvement over conventional metallicmaterials, which will deform plastically when global strains exceed ˜1%and will not recover from such deformation.

The material of the present invention can be applied to a wide range ofapplications, such as lightweight, multifunctional paneling foraircraft, automobiles, and other vehicles. For example, the reversibledeformation property is applicable to multi-cycle energy absorption,such as impact protection of vehicles. In such a mode, theultra-lightweight aspect would allow for its application without addedweight, while still filling space and allowing for a recoverabledeformation.

(3) Specific Details

As noted above and as shown in FIG. 1, the present invention is directedto an ultra-light micro-lattice 100 and a method for forming the same.To illustrate the ultra-light nature of the present invention, FIG. 1 isan illustration of the micro-lattice 100 resting atop the petals of adandelion flower 102. As can be appreciated by one skilled in the art,the micro-lattice 100 is incredibly light, so much so that it is able torest atop the dandelion flower 102 without crushing its petals. Theultra-light configuration of the micro-lattice 100 is provided due itsincredibly low-density design.

To explore the low-density design space that lattice structures offer, ametallic micro-lattice was fabricated according to the present inventionwith a periodic architecture of hollow tubes that connect at nodes,forming an octahedral unit cell (as shown in FIG. 1). The architectureand the fabrication process provided for a wall thickness of the hollowtubes as thin as 100 nm, resulting in a cellular material with a densityof 0.9 mg/cc. The density is calculated using the weight of the solidstructures, but not including the weight of the air in the pores,adhering to standard practice for cellular materials. The density of airat ambient conditions, 1.2 mg/cc, would need to be added to express thedensity of the solid-air composite. In this case, the present inventionprovides for an ultra-light cellular material having a relative densityin a range of 0.001% to 0.3%. The relative density is the ratio of thedensity (mass of a unit volume) of a substance or object to the densityof a given reference material, in this case the constituent materialwhich comprises the micro-lattice (such as the hollow tubes).

FIG. 2 illustrates how the micro-lattice architecture can be distilledinto three levels of hierarchy at three distinct length scales: unitcell (˜mm-cm) 200, hollow tube lattice member (˜μm-mm) 202 (i.e., hollowtubes or struts) and hollow tube wall (˜nm-μm) 204. Each architecturalelement can be controlled independently providing exceptional controlover the design and properties of the resulting micro-lattice.

With the process of the present invention (described below), unit cellsize and topology, hollow tube diameter and wall thickness can bealtered independently; when combined with conformal thin-film coatingmethods, micro-lattice structures with a wide range of constituentcompositions and micro-structures become available. The architecturedetermines the relative density of the lattice, and the film materialthen dictates the absolute density. The extraordinary control overarchitecture facilitates de-coupling historically linked properties—likedensity and stiffness—by allowing independent tailoring of specificproperties. For example the compressive modulus of these micro-latticescan be altered by modifying the inclination angle without changing thedensity significantly (See Literature Reference No. 11). The method todesign the micro-lattice architecture at multiple scales from nm to cmallows significantly more control than typical methods for formingultra-lightweight materials, especially foams and aerogels, wherenominally random processes govern porosity formation.

As shown in FIG. 3, the micro-lattice templates were fabricated using aself-propagating photopolymer waveguide technique reported previously(See Literature Reference No. 12), whereby a suitable liquidphotomonomer 300 is exposed to collimated UV light 302 through apatterned mask 304, producing an interconnected three-dimensionalphotopolymer lattice 306. A non-limiting example of a suitable liquidphotomonomer 300 is a thiol-ene resin.

With this method, a wide array of different architectures with unitcells in the 0.1 to >10 mm range can be made by altering the mask 304pattern and the angle of the incident light (See Literature ReferenceNo. 13). As a non-limiting example, architectures can be generated with1-4 mm lattice member length L, 100-500 μm lattice member diameter D,100-500 nm wall thickness t, and 60° inclination angle θ, similar to themicro-lattices depicted in FIG. 2.

It should be noted that the polymer lattice 306 is an open cellulartemplate. After the polymer lattice 306 is generated, films (e.g.,conformal nickel-phosphorous thin films) were deposited on the polymerlattices 306 by electroless plating 308 and the polymer was subsequentlyetched out 310 (via chemical etching or any other suitable etchingtechnique that is gentle enough not to destroy the micro-lattice). Theetchant has to be selective with respect to the template and the coatingmaterial, i.e., the etching rate of the template needs to besubstantially faster than that of the coating. For nickel coatings onthiol-ene templates, sodium hydroxide solution is the preferred etchant,for other material combinations, organic solvents, plasma etching,thermal pyrolysis or other etchants are favored. Freeze drying is usedfor fragile micro-lattices that are deformed by capillary forces onremoval from solution.

The auto-catalytic electroless nickel plating reaction enablesdeposition of thin films with controlled thickness on complex shapes andinside pores without noticeable mass transport limitations. Bycontrolling reaction time, a wall thickness of 100 nm can be achievedwhile maintaining a uniform conformal coating. The resulting ultra-lightmicro-lattice 312 essentially translates the deposited nano-scale thinfilm in three dimensions to form a macroscopic material where the basestructural elements are hollow tubes (as shown in FIG. 2). It should benoted that any suitable material can be deposited on the polymer lattice306, non-limiting examples of which include nickel, zinc, chrome, tin,copper, gold silver, platinum, rhodium, aluminum, a ceramic, including,diamond, diamond like carbon, alumina, zirconia, tin oxide, zinc oxide,silicon carbide, silicon nitride, titanium nitride, tantalum nitride,tungsten nitride, a polymer including parylene or combinations or alloysthereof, including multi-layers of different materials.

Transmission electron microscopy (TEM) revealed that the as-depositedelectroless nickel thin films are nano-crystalline, with ˜7 nm grainsizes consistent with literature reports (See Literature Reference No.14). Energy-dispersive X-ray spectroscopy confirmed that the compositionof the deposit is 7% phosphorous and 93% nickel by weight. Since thefilms were not annealed after deposition, they remained as asupersaturated solid solution of phosphorous in crystallineface-centered cubic (fcc) nickel lattice with no Ni₃P precipitatespresent (See Literature Reference No. 14). The 7 nm grain size renderselectroless nickel thin films harder and more brittle than typical nano-and micro-crystalline nickel. A hardness of 6 GPa and modulus of 210 GPawere measured by nano-indentation and hollow tube compressions (SeeLiterature Reference Nos. 15 and 16).

Micro-lattices with these extreme low densities exhibit uniquemechanical behavior. Compression experiments on micro-lattices showrecovery flow strains exceeding 50%.

FIGS. 4A through 4D provide images of a micro-lattice sample 400 with 14mg/cc (L: 1050 μm, D: 150 μm, t: 500 nm) during compression testingwhile FIG. 5A conveys the corresponding stress-strain curve measured ata prescribed displacement rate of 10 μm/sec. In these experiments, thesample was not attached to face sheets or the compression platens at thebottom or the top. FIG. 4A depicts the micro-lattice sample 400 prior tocompression. As shown in FIG. 4B, upon first compression, the latticeexhibits a compressive modulus of 529 kPa, with deviations from linearelastic behavior starting at a stress of 10 kPa. The stress decreasesslightly after the peak associated with buckling and node fractureevents, and a broad plateau is subsequently formed in the stress-straincurve as buckling and localized node fracture events spread through thelattice. FIG. 4C shows the micro-lattice at 50% compression. Uponunloading, the stress drops rapidly but does not approach zero until theplaten is close to its original position. After removing the load, themicro-lattice recovers to 98.6% of its original height and resumes itsoriginal shape (as shown in FIG. 4D). For further illustration, FIGS. 4Ethrough 4H provide images of the micro-lattice sample through itscompression and recovery. More specifically, FIG. 4E is an optical imageof a unit cell of the micro-lattice, in an unloaded or uncompressedcondition. FIG. 4F is an optical image of the unit cell, depicting howthe unit cell accommodates compressive strain by buckling at the nodes.FIG. 4G is a scanning electron microscopy (SEM) image of a node beforetesting, while FIG. 4H is an SEM image of the node after six compressioncycles at 50% strain.

Interestingly, the stress-strain behavior corresponding to the 1^(st)cycle is never repeated during subsequent testing. Rather, during asecond compression, the peak stress is absent and the ‘pseudo-hardening’behavior changes, but the stress level achieved at 50% strain is only10% lower than that after the first cycle. Consecutive compressioncycles exhibit stress-strain curves nearly identical to the secondcompression.

As shown in FIG. 5B, stiffness and strength diminish with cycle number,but are almost constant after the third cycle (as shown in FIG. 5B). Themicro-lattice shows significant hysteresis during compressionexperiments, allowing a measurement of the energy absorption, which isestimated to be 2.2 mJ for the first cycle. After three cycles a nearlyconstant energy loss coefficient of ˜0.4 is calculated by dividing theabsorbed energy by the total energy required for compression (as shownin FIG. 5B).

FIG. 5C shows the stress-strain curves of the first two compressioncycles of a sample with a density of 1 mg/cc and larger unit cells (L: 4mm, D: 500 μm, t: 120 nm) illustrating similar behavior of differentmicro-lattices in the ultra-low density regime. Increasing the densityand wall thickness will eventually lead to compression behavior moretypical for metallic cellular materials. FIG. 5D shows the compressionof a sample with 43 mg/cc (L: 1050 μm, D: 150 μm, t: 1400 nm): noticethat strain recovery upon unloading from 50% strain is essentiallyabsent.

Optical examination of the ultra-light micro-lattices during deformationsuggests that deformation initiates by Brazier buckling at the nodes (asshown in FIGS. 4E and 4F) (See Literature Reference No. 17). A closerinspection of the micro-lattices by SEM shows that cracks and wrinklesare introduced primarily at the nodes during 50% compression (as shownin FIGS. 4G and 4H). This damage is responsible for the 1-2% residualstrain observed after the first compression cycle, and the drop in theyield strength and modulus during subsequent compression cycles. Oncestable relief cracks form at the nodes, the bulk micro-lattice materialcan undergo large compressive strains without enduring further fractureor plastic deformation in the solid nickel-phosphorous material, thusexhibiting the reversible compressive behavior shown in FIGS. 4A through5D. While the precise details concerning the deformation mechanism arecurrently under investigation, it is clear that the extremely smallaspect ratio of the hollow tube wall to diameter plays a key role in thenearly full recoverability, by allowing truss members to undergo largerotations about remnant nodal ligaments without accumulation ofsignificant plasticity. Increasing this aspect ratio leads to excessivefracture and loss of the recoverable deformation behavior (as shown inFIG. 5D).

Although similar stress-strain curves as presented in FIG. 5A aretypical for foams of viscoelastic polymer (See Literature Reference No.18) and carbon nanotube forests (See Literature Reference No. 19), theyare unprecedented for metal-based materials. Two energy loss mechanismscould possibly explain the energy dissipation during compression cycles:(1) Structural damping due to snapping events (e.g., kinking, or Brazierbuckling of the trusses) and (2) Mechanical or Coulomb friction throughmembers in contact (or a combination of both). This mechanical behavioris especially surprising considering the relatively brittle nature ofthe constituent material. The electroless nickel thin films are found tobe brittle, as evidenced by the formation of cracks near a residualindentation mark (as shown in FIG. 5E) and the rapid collapse uponsingle hollow truss member compressions (See Literature Reference No.15). Specifically, FIG. 5E is an SEM micrograph of post-nanoindentationmark in a 500 nm-thick electroless nickel film, demonstrating brittlebehavior. This is likely due to the ultra-fine grain sizes of ˜7 nm thathinder plastic deformation by dislocation motion (See LiteratureReference No. 20).

However, the micro-lattices exhibit completely different bulkproperties: the cellular architecture effectively transforms the brittlethin-film property into a ductile and super-elastic lattice behavior byenabling sufficient freedom for deformation and tolerance to localstrains, such as forming relief cracks that are stable during repeatedcompression cycles, while still maintaining the structure to remaincoherent. Hence, cellular material architecture can fundamentally changethe material properties and generate functional ductility and functionalsuperelasticity at the bulk scale.

Although the present invention has demonstrated formation of thelightest known material to date, micro-lattice materials with even lowerdensity could be fabricated by following the same methodology. Thedensity of the synthesized micro-lattices can be approximated by:

$\begin{matrix}{\rho = {\frac{2\;\pi}{\cos^{2}{\theta sin}\;\theta}\left( \frac{D}{L} \right)\left( \frac{t}{L} \right)\rho_{s}}} & (1)\end{matrix}$where ρ_(s)is the density of the constituent material. The wallthickness t reaches a minimum at 100 nm with the current fabricationprocess because it requires a continuous and robust film that canwithstand the mechanical forces associated with removal of the polymertemplate. Naturally, the density decreases with increasing cell size, orlattice member length L. By increasing L four-fold and keeping L/Droughly constant, the density was decreased by approximately the samefactor, suggesting that it is possible to attain further reductions indensity with even larger cell sizes. Achievable densities will belimited by the mechanical stability of the micro-lattice structure bothduring processing and against ambient loading (e.g. gravity, aircurrents).

To assess the mechanical stability limit, it is assumed that thecompressive strength of the lattice scales with the local bucklingstrength, σ_(lb), of the hollow tubes (See Literature Reference No. 21):

$\begin{matrix}{\sigma_{lb} = {\frac{2\; E_{s}}{\sqrt{3\left( {1 - v_{s}^{2}} \right)}}\left( \frac{t}{D} \right)}} & (2)\end{matrix}$where E_(s) is the Young's modulus and v_(s) the Poisson's ratio of thesolid constituent material.

Using the micro-lattice with 1 mg/cc and a strength of 29 Pa in FIG. 5Cas a reference, the density of similar micro-lattices with t=100 nm andL/D=8 could be reduced to 0.2 mg/cc by increasing L to 2 cm whilemaintaining a compressive strength of 3 Pa. The density could be pushedlower with a constituent thin film material with a higher specificstiffness and strength. Diamond may be among the best candidates withits extremely high stiffness and strength and well established vapordeposition routes enabling films with <50 nm thickness (See LiteratureReference No. 20). The calculated density of diamond micro-lattices with50 nm wall thickness and L/D=8 is 0.01 mg/cc, which represents afivefold reduction in density by switching from nickel to diamond.

As described herein, by designing architecture of hollow-tubemicro-lattice materials at three levels of structural hierarchy,unprecedented mechanical properties and low densities can be achieved,redefining how light a material can be. Extending this approach to othermaterials deposited by e.g. atomic layer deposition (ALD)electrophoretic deposition (EPD) or chemical vapor deposition (CVD) anddeveloping appropriate computational tools for architecture optimizationwill undoubtedly lead to additional extraordinary cellular materialsthat further redefine the limits of low-density materials.

(4) Fabrication Example

(4.1) Polymer Micro-Lattice Fabrication

Polymer micro-lattice templates were fabricated from an interconnectedpattern of self-propagating photopolymer waveguides as described indetail elsewhere (See Literature Reference Nos. 12 and 13). Prior toelectroless plating, samples were thermally post-cured at 120° C. in airfor 12 hrs.

(4.2) Hollow Nickel Micro-Lattice Formation

The polymer micro-lattice template samples were then used as directtemplates for electroless nickel plating using a commercially availableprocess, such as that provided by OM Group Inc., located at 127 PublicSquare, 1500 Key Tower, Cleveland, Ohio 44114. To prepare the surfacefor electroless deposition, the polymer sample were first heat treatedat greater than 120 degrees Celsius and then immersed in 1 molar sodiumhydroxide solution, then palladium catalyst was deposited by immersionin activator solution containing hydrochloric acid and tin(II) chloride(Fidelity 1018, OM Group Inc.), followed by an etch in acceleratorsolution containing fluoboric acid (Fidelity 1019, OM Group Inc.). Thesamples were then immersed in electroless nickel plating solution withnickel sulfate as nickel source, sodium hypophosphite as reducing agent,and sodium malate and acetic acid as complexing agents (9026M, OM GroupInc.). The electroless nickel plating bath was kept at pH 4.9 byaddition of ammonium hydroxide and plating was performed at 80° C.Different plating times were chosen to achieve different coatingthicknesses (as reported in FIG. 6). A wall thickness of 500 nm wasachieved by electroless nickel plating of approximately 3 minutes. Afternickel deposition the top and bottom surface of each sample was sandedto expose the underlying polymer at each node. The polymer was thenchemically etched in a base solution (3M NaOH at 60° C.) for 24 hours,creating the hollow tube nickel micro-lattice samples in FIG. 2. Sampleswith wall thickness below ˜150 nm could not be removed from the aqueousNaOH solution directly because the capillary forces deformed thelattice. In these cases, the samples were freeze dried after exchangingthe NaOH solution to deionized water and then to t-butanol.

It should be noted that the conditions during the chemical etch have tobe carefully adjusted to provide enough agitation to dissolve thepolymer in the hollow tubes but limit the forces acting on themicro-lattice to avoid fracture. Successful etching conditions wereachieved by inserting shields around the micro-lattice to protect itfrom the solution flow. Below as certain wall thickness, depending onthe architecture, the micro-lattice is too fragile to remove them fromthe liquid. In this case freeze drying is employed to remove the liquid.As noted above, a solvent exchange was performed to exchange the aqueousNaOH solution with t-Butanol and subsequently the t-Butanol containingthe micro-lattice is frozen. T-Butanol exhibits a much lower volumechange on freezing than water resulting in less damage to themicrolattice. A vacuum is then applied to sublimate the t-butanolleaving a dry micro-lattice of the present invention behind.

What is claimed is:
 1. A micro-lattice, comprising: four or more layersof truss, each layer of truss having a plurality of truss members thatintersect with one another, the truss members formed of hollow tubes;wherein the micro-lattice is formed of a material and having a relativedensity in a range of 0.00001 to 0.0005 in relation to the theoreticaldensity of the material; wherein the hollow tubes have a diameter suchthat the diameter is between 10 and 1000 microns; and wherein the hollowtubes are formed by tube walls having a wall thickness between 0.01 and2 microns.
 2. The micro-lattice as set forth in claim 1, wherein thehollow tubes have a diameter such that the diameter is between 100 and500 microns; and wherein the hollow tubes have a wall thickness between0.1 and 0.5 microns.
 3. The micro-lattice as set forth in claim 2,wherein the micro-lattice recovers from deformations in height in arange of 50% to 90%, where the deformations in height is expressed asheight of the micro-lattice as deformed divided by a height of themicro-lattice before deformation.
 4. The micro-lattice as set forth inclaim 3, wherein the hollow tubes are formed of a material selected froma group consisting of nickel, zinc, chrome, tin, copper, gold silver,platinum, rhodium, aluminum, a ceramic, diamond, diamond like carbon,alumina, zirconia, tin oxide, zinc oxide, silicon oxide, siliconcarbide, silicon nitride, titanium nitride, tantalum nitride, tungstennitride, a polymer, parylene, or any combination or alloy thereof. 5.The micro-lattice as set forth in claim 1, wherein the micro-latticerecovers from deformations in height in a range of 2% to 90%, where thedeformations in height is expressed as height of the micro-lattice asdeformed divided by a height of the micro-lattice before deformation. 6.The micro-lattice as set forth in claim 1, wherein the hollow tubes areformed of a material selected from a group consisting of nickel, zinc,chrome, tin, copper, gold silver, platinum, rhodium, aluminum, aceramic, diamond, diamond like carbon, alumina, zirconia, tin oxide,zinc oxide, silicon oxide, silicon carbide, silicon nitride, titaniumnitride, tantalum nitride, tungsten nitride, a polymer, parylene, or anycombination or alloy thereof.